You can have a look at the SWT_AWT class which uses WEmbeddedFrame.
However, there are many conditions associated with this:
1) It only works on Windows. Swing/AWT ships with a library that is linked in such a way that it does not export its X/motif libraries and this causes a problem where globals are concerned since SWT tries to use the same libraries.
2) It does not work with light weight widgets. There are issues with the keystrokes getting sent to the light weight widget.
3) It is experimental (in the internal package org.eclipse.swt.internal.awt.win32) and therefore the API may change.